We wish to extend this approach so that both the strain field and the stress-free lattice spacing can be estimated.
As the measurements are a non-linear function of the unknowns we cannot directly apply the standard Gaussian process regression methods [1]}.
There exists several approaches to approximate Gaussian processes for non-linear functions; the Laplace approximation [1]}, [3]}, GP variational inference [4]}, and Markov Chain Monte Carlo methods (such as Elliptical Slice Sampling [5]}).
For these methods, the measurements are modelled as non-linear functions of the GP sampled at the measurement locations (known as latent function values). The latent function values that bestFor a given criterion of best fit, whether it be marginal log likelihood, cross-validation, etc. match the data are determined by one of the above methods. Then, Gaussian process regression is applied with the latent function values taking the place of measurements to determine the function values at the new locations of interest.
